The Spanish champions progressed from the last 16 in the 10th consecutive season against all odds, winning 6-5 on aggregate and overturning a 4-0 deficit from the first leg in France.
Needing to score at least five goals, Barcelona were 2-0 up at half-time after Luis Suarez's opener and Layvin Kurzawa's own-goal, before Lionel Messi put them further in front.
Edinson Cavani thought he had dashed hopes of a fightback when he netted a crucial away goal for PSG but Neymar had other plans as he played a crucial part in three Barcelona goals in seven agonising minutes to rescue the tie, scoring twice and assisting Sergi Roberto's clincher.
And Luis Enrique revealed after the match that he was always confident in the quality of his players and their ability to go through, hailing their winning mentality in the end.
"It was an incredible night. We won a game that I thought was impossible," the coach told Mediaset Premium. "When they made it 3-1, it looked over but the end of the game was spectacular. We are very happy.
"When you have a team like this, made up of champions, that have won every title, everything is possible."
The landslide loss at Parc des Princes several weeks ago had been a major catalyst in Luis Enrique's announcement that he would be departing the club at the end of the season.
But, despite the turnaround, the 46-year-old insists he will not renege on his decision that he needs a sabbatical after his three-season spell in the Camp Nou dugout
"Convince me to stay on? That decision is done!" he concluded.